Chapter 15

Economic Efficiency

POSITIVE VS NORMATIVE

Positive statements are statements about
what is; normative statements are statements about what ought
to be. Economics is a positive science. An economist who says
(correctly or incorrectly) that a one-dollar increase in the minimum
wage will increase the unemployment rate by half a percentage point
is expressing his professional opinion. If he goes on to say,
"Therefore we should not increase the minimum wage," his statement is
no longer only about economics. In order to reach a "should"
conclusion, he must combine opinions about what is, which are part of
economics, with values, opinions about what ought to be, which
are not.

Of course, one of the main reasons people learn
what is is in order to decide what ought to be. Economists have
values just as everyone else does. Those values affect both their
decision to become economists instead of ditchdiggers or political
scientists and the questions they choose to study. But the values
themselves, and the conclusions that require them, are not part of
economics.

Economists frequently use terms, such as
"efficient," that sound very much like "ought" words. Once one has
proved that something leads to greater efficiency, it hardly seems
worth asking whether it is desirable. Such terms, however, have a
precise positive meaning, and it is quite easy to think of reasons
why efficiency in the economist's sense might not always be
desirable.

My own interpretation of why we use such terms is
as follows. People keep coming to economists and asking them what to
do. "Should we have a tariff?" "Should we expand the money supply?"
The economist answers, "Should? I don't know anything about 'should.'
If you have a tariff, such and such will happen; if you expand the
money supply, . . ." The people who ask the questions say, "We don't
want to know all that. On net, are the results good or bad?" The
economist finally answers as follows:

As an economist, I have no expertise in
good and bad. I can, however, set up a "criterion of goodness"
called efficiency, that has the following characteristics. First,
it has a fairly close resemblance to what I suspect you mean by
"good." Second, it is so designed that in many cases I can figure
out, by economics, whether some particular proposal (such as a
tariff) is an improvement in terms of my criterion. Third, I
cannot think of any alternative criterion closer to what I suspect
you mean that also has the second characteristic.

One could object that the economist, defining
efficiency according to what questions he can answer rather than what
questions he is being asked, is like the drunk looking for his wallet
under the street light because the light is better there than where
he lost it. The reply is that an imperfect criterion of desirability
is better than none.

The point of this story is to show how it is that
economists claim to be positive scientists yet frequently use
normative-sounding words. Three of these words are "improvement,"
"superior," and "efficient." They are used in a number of different
ways in economics, and it is easy to confuse them.

IMPROVEMENT AND EFFICIENT

While the terms "improvement," "superior," and
"efficient" are used in a number of different ways in different
contexts--we shall discuss five in this chapter--the three words
always have the same relation to each other. An improvement is
a change--in what is being produced, in how it is produced, in who
gets it, or whatever--that is in some way desirable. Situation B is
superior to situation A if going from A to B is an
improvement. A situation is efficient (in some particular
respect) if it cannot be improved--if, in other words, there is no
possible situation that is superior to it.

We will start by explaining what it means to
produce one good efficiently. The next step is to apply the concept
to two goods produced for one individual, seeing in what sense
producing more of one and less of the other might be a net
improvement. The final and most difficult step is to apply the idea
of efficiency to something that affects two or more
people.

Production Efficiency

We start with production efficiency. An
improvement in production means using the same inputs to produce more
of one output without producing less of another (output
improvement), or producing the same outputs using less of one
input and no more of any other (input improvement). As long as
both inputs and outputs are goods, an improvement in this sense is
obviously desirable; it means you have more of one desirable thing
without giving up anything else. An output process is production
efficient (sometimes called X-efficient) if there is no
way of changing it that produces an output or input improvement.
Production improvements and production efficiency provide a way of
evaluating different outcomes that does not depend on our knowing the
relative value of the different goods to the consumer. As long as
both are goods, a change that gives more of one without less of the
other is an improvement.

Figure 15-la shows a production possibility set
for producing two goods, X and Y, using a fixed quantity of inputs;
every point in the shaded region represents a possible output bundle.
The curve F is the frontier of the set; for any point in the set that
is not on F (such as A), there is some point on the frontier (B) that
represents an improvement; in the case illustrated, B contains more
of both X and Y than A. The points on the frontier are all output
efficient; starting at B, the only way to produce more X is by
producing less Y, as at C, and the only way to produce more Y is by
producing less X, as at D.

This is the first time I have talked about the
idea of production efficiency, but not the first time I have used it.
From Chapter 3 on, I have been drawing figures with possibility sets
and frontiers. A budget line, for example, is the frontier of a
possibility set--the set of bundles it is possible to purchase with a
given income. In indifference curve analysis, we only consider points
on the budget line, not points below it, even though points below it
are also possible--we could always throw away part of our income.
Figure 15-1b shows this. The shaded area is the consumption
possibility set. The line B is the consumption possibility
frontier, alias the budget line.

Possibility sets and frontiers. Figure
15-la shows a production possibility set; F is its frontier. Figure
15-1b shows the set of alternative bundles available to a consumer;
the budget line B is its frontier.

But since insatiability implies that there is
always something we want more of, we would never choose to throw away
part of our income. Any point in the interior of the possibility set
is dominated by a point on the frontier representing a bundle with
more of both goods. Point K on Figure 15-1b is dominated by point L,
just as A is dominated by B on Figure 15-1a. So if we are looking for
the best bundle, we need only consider points on the
frontier.

Similar considerations explain why, in diagrams
such as Figures 5-9a and 5-9b of Chapter 5, we only considered output
bundles on the frontier of the production possibility set (the number
of lawns that could be mowed and meals cooked or ditches dug and
sonnets composed with a given amount of labor). If you are going to
work that number of hours, you might as well get as much output as
possible, not spend some of the time walking around in circles
instead of either mowing lawns or cooking meals.

Utility Efficiency

So long as we only consider output efficiency,
there is no way of choosing between points B, C, and D on Figure
15-la, all of which are output efficient. To do that, we must
introduce preferences. Figure 15-2a is Figure 15-la with the addition
of a set of indifference curves. If I am producing X and Y for my own
consumption, I can use my indifference curves to compare different
efficient points. Point D, for example, is on a higher indifference
curve than point C; I would rather consume 5 units of Y and 2 of X
(point D) than 3 units of Y and 4 of X (point C).

A utility improvement is a change that
increases my utility--moves me to a higher indifference curve. A
situation is utility efficient if no further such improvements
are possible. On the diagram, point E is the only point in the
production possibility set that is utility efficient.

The fact that one point is output efficient and
another is not does not mean that the first point is either output or
utility superior to the second. On the diagram, point C is output
efficient and point A is not--but A is on a higher indifference curve
than C! A is inefficient because B is superior to it (more of both X
and Y). B is also on a higher utility curve than A; it must be, since
X and Y are both goods. C is efficient not because it is output
superior to A (it is not--C has more X but less Y, so neither is
output superior to the other) but because nothing is output superior
to it. Since C is not output superior to A, there is no reason why it
cannot be utility inferior to it--and in fact it is. If someone
argued that "You should produce at C instead of at A, since C is
efficient and A is not," his argument would sound plausible but be
wrong.

On first reading, the previous paragraph may seem
both confusing and irrelevant. It is there because the same point
will be crucial to understanding the use (and misuse) of another and
very important form of improvement and efficiency--Pareto
efficiency--which I shall describe later in the chapter. The relevant
concept--that the fact that A is not efficient and C is does not
imply that C is an improvement on A--is easier to understand in the
context of output efficiency than in the context of Pareto
efficiency, so I advise you to try to understand it at this
point.

Efficient and inefficient outcomes. On
Figure 15-2a, the alternatives are different output bundles to be
consumed by an individual whose tastes are shown by the indifference
curves; on Figure 15-2b, they are different allocations of goods (and
hence utility) to two individuals. In each case, points on the
frontier are efficient and points not on the frontier are not, but
the former are not necessarily superior to the latter.

SUMMING UTILITIES: THE
PROBLEM

So far, we have been considering changes that
affect only one person. The fundamental problem in defining what
economic changes are, on net, improvements is the problem of
comparing the welfare of different people. If some change results in
my having two more chocolate chip cookies and one less glass of Diet
Coke, there is a straightforward sense in which that is or is not an
improvement; I do or do not prefer the new set of goods to the old
(utility improvement). But what if the change results in my having
two more cookies and your having one less glass of Diet Coke?
It is an improvement from my standpoint, but not from
yours.

The usual solution to this problem is to base the
definition of efficiency on the idea of a Pareto improvement
(named after the Italian economist Vilfredo Pareto)--defined as a
change that benefits one person and injures nobody. A system is then
defined as Pareto efficient if there is no way it can be
changed that is a Pareto improvement. The problem with this approach
is that it leaves you with no way of evaluating changes that are not
Pareto improvements; the attempt to get around that problem while
retaining the Paretian approach leads to serious problems, which I
will discuss later.

One reason so many examples in earlier chapters
involved identical producers and identical consumers was that I
wanted to avoid the problem of balancing a loss to one person against
a gain to another. If everyone is identical, any change that is in
any sense an improvement must be a Pareto improvement: if it benefits
anyone, it must benefit everyone. Early in the book, with the
discussion of efficiency still many chapters in the future, that was
very convenient.

Output efficiency is analogous to Pareto
efficiency, with different people's utilities in the latter case
corresponding to outputs of different goods in the former. A
situation is Pareto efficient if there is no way of changing it that
benefits one person and harms nobody--increases someone's utility
without decreasing anyone else's. A situation is output efficient if
there is no way of changing it that increases one output without
decreasing some other output. Figure 15-2b shows the similarity; the
axes are my utility and your utility, the region R consists of all
possible combinations (the utility possibility set), and the
frontier of that region, the curve F, consists of all the
Pareto-efficient combinations.

In the case of output, we have a common measure by
which to compare various points on the boundary: the utility of the
individual consuming the output. This lets us compare two alternative
output bundles, one of which contains more of one output and less of
another. The important difference between Figure 15-2b and Figure
15-2a is the absence of indifference curves on 15-2b. The problem in
comparing outcomes that affect several people is that there is no
obvious way of comparing two different outcomes, one of which
produces more utility for me and less for you than the
other.

Some economists have tried to deal with such
problems by imagining a social equivalent of the individual utility
function (called a social welfare function). A social welfare
function would give the welfare of the whole society as a function of
the utilities of individuals, just as the utility function gives the
welfare of the individual as a function of the quantities of goods he
consumes. If we knew the social welfare function for the two-person
society shown on Figure 15-2b, we could draw a set of social
indifference curves on Figure 15-2b, just as we drew individual
indifference curves on Figure 15-2a.

If we assume there is a social welfare function,
we can try to analyze the outcome of different economic arrangements
in terms of social preferences without actually knowing what the
social preferences are--just as we have analyzed situations involving
individual preferences without knowing what any particular real-world
individual's preferences actually are. Some of the difficulties with
this approach are discussed in the optional section of this
chapter.

PARETIAN
AND MARSHALLIAN EFFICIENCY

Another way of approaching the problem is to claim
that although we have no way of deciding which of two
Pareto-efficient outcomes is preferable, at least we should prefer
efficient outcomes to inefficient ones. This argument is often made
and sounds reasonable enough, but it runs into the difficulty that I
discussed earlier in the context of output efficiency. While we may
all agree that a Pareto improvement is an unambiguously good thing,
it does not follow that a situation that is Pareto efficient is
superior to one that is not.

Consider a world of two people, you and me, and
two goods, cookies and Diet Cokes (20 of each). The situation is
shown on Figure 15-2b; the axes are not Diet Cokes and cookies but my
utility (which depends on how many of the Diet Cokes and cookies I
have) and your utility (which depends on how many you have). One
possible situation (A on Figure 15-2b) is for you to have all the
cookies and all the Diet Cokes. That is Pareto efficient; the only
way to change it is to give me some of what you have, which makes you
worse off and so is not a Pareto improvement. Another possible
situation (B) is for each of us to have 10 cookies and 10 Diet Cokes.
That may be inefficient; if I like cookies more, relative to Diet
Cokes, than you do, trading one of my Diet Cokes for one of your
cookies might make us both better off (move us to C). The first
situation is (Pareto) efficient and the second is not, yet it seems
odd for you to say that the first situation is better than the second
and expect me to agree with you.

The problem is that situation B is inefficient not
because changing from B to A is a Pareto improvement (it is not) but
because changing from B to C (I have nine Diet Cokes and eleven
cookies, you have eleven Diet Cokes and nine cookies) is; it is hard
to see what that has to do with A being better than B.

As this suggests, there are serious difficulties
with the Paretian solution to the problem of evaluating different
outcomes. They are sufficiently serious to make me prefer a different
solution, proposed by the British economist Alfred Marshall; while he
did not use the term "efficiency," his way of defining an improvement
is an alternative to Pareto's, and I shall use the same terms for
both. In most practical applications, the two definitions turn out to
be equivalent, for reasons that I shall explain in the next section;
but Marshall's definition makes it clearer what "improvement" means
and in what ways it is only an approximate representation of what
most of us mean by describing some economic change as "a good thing,"
"desirable," or the like. I have introduced the Paretian definition
here because it is what most economics textbooks use; you will
certainly encounter it if you study more economics.

To understand Marshall's definition of an
improvement, we consider a change (the abolition of tariffs, a new
tax, rent control, . . .) that affects many people, making some worse
off and others better off. In principle we could price all of the
gains and losses. We could ask each person who was against the change
how much money he would have to be given so that on net the money
plus the (undesirable) effect of the change would leave him exactly
as well off as before. Similarly we could ask each gainer what would
be the largest amount he would pay to get that gain, if he had to. We
could, assuming everyone was telling us the truth, sum all of the
gains and losses, reduced in this way to a common measure. If the sum
was a net gain, we would say that the change was a Marshall
improvement. If we had a situation where no further (Marshall)
improvement was possible, we would describe it as
efficient.

This definition does not correspond perfectly to
our intuition about when a change is good (or makes people "on
average, happier") for at least two reasons. First, we are accepting
each person's evaluation of how much something is worth to him; the
value of heroin to the addict has the same status as the value of
insulin to the diabetic. Second, by comparing values according to
their money equivalent, we ignore differences in the utility of money
to different people. If you were told that a certain change benefited
a millionaire by an amount equivalent for him to $10 and injured a
poor man by an amount equivalent for him to $9, you would suspect
that in some meaningful sense $10 was worth less to the millionaire
than $9 to the poor man and therefore that "net human happiness" had
gone down rather than up. The concept of efficiency is intended as a
workable approximation of our intuitions about what is good; even if
we could make the intuitions clear enough to construct a better
approximation, it would still be less useful unless we had some way
of figuring out what changes increased or decreased it.

How do we find out what changes produce net
benefits in Marshall's sense? The answer is that we have been doing
it, without saying so, through most of the book. Consumer (or
producer) surplus is the benefit to a consumer (or producer) of a
particular economic arrangement (one in which he can buy or sell at a
particular price) measured in dollars according to his own
values.

Several chapters back, I showed that the area
under a summed demand curve was equal to the sum of the areas under
the individual demand curves. So when we measure consumer surplus as
the area under a demand curve representing the summed demands of many
consumers, we are summing benefits--measured in dollars--to many
different people. If we argue that some change in economic
arrangements results in an increase in the sum of consumer and
producer surplus, as we shall be doing repeatedly in the next few
chapters, we are arguing that it is an improvement in the Marshallian
sense.

The essential problem we face is how to add
different people's utilities together in order to decide whether an
increase in utility to one person does or does not compensate for a
decrease to another. Marshall's solution is to add utilities as if
everyone got the same utility from a dollar. The advantage of that
way of doing it is that since we commonly observe people's values by
seeing how much they are willing to pay for something, a definition
that measures values in money terms is more easily applied in
practice than would be some other definition.

Alfred Marshall was aware of the obvious argument
against treating people as if they all had the same utility for a
dollar: the fact that they do not. His reply was that while that was
a legitimate objection if we were considering a change that benefited
one rich man and injured one poor man, it was less relevant to the
usual case of a change that benefited and injured large and diverse
groups of people: all consumers of shoes and all producers of shoes,
all the inhabitants of London and all the inhabitants of Birmingham,
or the like. In such cases, individual differences could be expected
to cancel out, so that the change that improved matters in Marshall's
terms probably also "made things better" in some more general
sense.

There is another respect in which Marshall's
definition of improvement is useful, although it is one that might
not have appealed to Marshall. If a situation is inefficient, that
means that there is some possible change in it that produces net
(dollar) benefits. If so, a sufficiently ingenious entrepreneur might
be able to organize that change, paying those who lose by it for
their cooperation, being paid by those who gain, and pocketing the
difference. If, to take a trivial example, you conclude that there
would be a net improvement from converting the empty lot on the
corner into a McDonald's restaurant, one conclusion you may reach is
that the present situation is inefficient. Another is that you could
make money by buying the lot, buying a McDonald's franchise, and
building a restaurant.

MARSHALL, MONEY, AND REVEALED
PREFERENCE

There are several ways in which it is easy to
misinterpret the idea of a Marshall improvement. One is by concluding
that since net benefits are in dollars, "Economics really is just
about money." Dollars are not what the improvement is but only what
it is measured in. If the price of apples falls from $10 apiece to
$0.10 apiece and your consumption rises from zero to 10/week, you
have $1/week less money to spend on other things, but you are better
off by the consumer surplus on 10 apples per week--the difference
between what they cost and what they are worth to you. Money is a
convenient common unit for measuring value; that does not mean that
money itself is the only, or even the most important, thing valued.
The definition of a Marshall improvement does not even require that
money exist; all values could have been stated in apples, water, or
any other tradable commodity. As long as the price of apples is the
same for all consumers, anything that is a net improvement measured
in apples must also be a net improvement measured in money. If, for
instance, apples cost $0.50, a gain measured in apples is simply
twice as large a number as the same gain measured in dollars, just as
a distance measured in feet is three times the same distance measured
in yards.

A second mistake is to take too literally the idea
of "asking" everyone affected how much he has gained or lost. Basing
our judgments on people's statements would violate the principle of
revealed preference, which tells us that values are measured by
actions, not words. That is how we measure them when analyzing what
is or is not a Marshall improvement. Consumer surplus, for example,
is calculated from a demand curve, which is a graph of how much
people do buy at any price, not how much they say they think they
should buy.

If we decided on economic policy by asking people
how much they valued things, and if their answers affected what
happened, they would have an incentive to lie. If I really value a
change (say, the imposition of a tariff) at $100, I might as well
claim to value it at $1,000. That will increase the chance that the
change will occur, and in any case I do not actually have to pay
anything for it. That is why, in defining a Marshall improvement, I
added the phrase "assuming everyone was telling us the truth." What
they were supposed to be telling the truth about was what they would
do--how much they would give, if necessary, in order to get the
result they preferred.

MARSHALL DISGUISED AS PARETO

The conventional approach to economic efficiency
defines a situation as (Pareto) efficient if no Pareto improvements
are possible in it. At first glance, that definition appears very
different from the one I have borrowed from Marshall, which compares
losses and benefits measured in dollars and defines a situation as
efficient if no net improvement can be made in it. The Paretian
approach appears to avoid any such comparison by restricting itself
to the unobjectionable statement that a change that confers only
benefits and no injuries is an improvement. The problem comes when
one tries to apply this definition of efficiency to judging
real-world alternatives.

Consider the example of tariffs. The abolition of
tariffs on automobiles would make American auto workers and
stockholders in American car companies worse off. Buyers of cars and
producers of export goods would be better off. It can be shown that
under plausible simplifying assumptions, there exists a set of
payments from the second group to the first that, combined with the
abolition of tariffs, would leave everyone better off. The payments
by members of the second group would be less than their gain from the
abolition; the receipts by members of the first group would be more
than their losses from abolition.

This is equivalent to showing, as I shall do in
Chapter 19, that the dollar gains to the members of the second group
total more than the dollar losses to the members of the first
group--that the abolition of tariffs is an improvement in Marshall's
sense of the term. If I gain by $20 and you lose by $10, it follows
both that there is a net (Marshall) improvement and that if I paid
you $15 the payment plus the change would leave us both better off
(by $5 each), making it a Pareto improvement. So a Marshall
improvement plus an appropriate set of transfers is a Pareto
improvement; and any change that, with appropriate transfers, can be
converted into a Pareto improvement must be a Marshall
improvement.

The abolition of auto tariffs by itself, however,
is not a Pareto improvement: auto workers and stockholders are worse
off. How then can Pareto efficiency be used to judge whether the
abolition of tariffs would be a good thing? By the following magic
trick.

The abolition of tariffs plus appropriate payments
from the gainers to the losers would be a Pareto improvement. Since
the situation with tariffs could be Pareto improved (by abolition
plus compensation), it is not efficient. The situation without
tariffs cannot be Pareto improved (I have not proved this; assume it
is true). Hence abolition of tariffs moves us from an inefficient to
an efficient situation. Hence it is an improvement.

If you believe that, I have done a bad job of
explaining, earlier in this chapter, why a movement from an
inefficient to an efficient situation need not be an improvement--a
point made once in the context of output efficiency and again in the
context of Pareto efficiency. A world without tariffs (and without
compensation) is efficient, and a world with tariffs is not; but it
does not follow that going from the latter to the former is an
improvement. The situation with the tariff is being condemned not
because it is Pareto inferior to the situation without the tariff but
because it is Pareto inferior to yet a third situation: abolition of
the tariff plus compensating payments.

Half of the trick is in confusing "going from a
Pareto-inefficient to a Pareto-efficient outcome" with "making a
Pareto improvement." The other half is in the word "possible."
Arranging the compensating payments necessary to make the abolition
of tariffs into a Pareto improvement may well be impossible (or
costly enough to wipe out the net gain), since there is no easy way
of discovering exactly who gains or loses by how much. If so, then
the Pareto improvement is really not possible, so the initial
situation is not really Pareto inefficient. The concept of Pareto
improvement, and the associated definition of efficiency, can be
applied to judge many real-world situations inefficient if you assume
that compensating payments can be made costlessly (i.e., with no cost
other than the payments themselves). Without this assumption, which
is usually not made explicit, the Paretian approach is of much more
limited usefulness.

One way to get out of this trap while retaining
the trappings of the Paretian approach is to describe the abolition
of the automobile tariff (without compensation) as a potential
Pareto improvement or Kaldor improvement, meaning that it
has the potential to be a Pareto improvement if combined with
appropriate transfers (the compensation principle--it is an
improvement if the gainers could compensate the losers, even though
they don't). This, as I pointed out above, is equivalent to saying
that it is an improvement in Marshall's sense.

I prefer to use the Marshallian approach, which
makes the interpersonal comparison explicit, instead of hiding it in
the "could be made but isn't" compensating payment. To go back to the
example given earlier, a change that benefits a millionaire by $10
and costs a pauper $9 is a potential Pareto improvement, since if
combined with a payment of $9.50 from the millionaire to the pauper
it would benefit both. If the payment is not made, however, the
change is not an actual Pareto improvement. The "potential Paretian"
approach reaches the same conclusion as the Marshallian approach and
has the same faults; it simply hides them better. That is why I
prefer Marshall. From here on, whenever I describe something as an
improvement or an economic improvement, I am using the term in
Marshall's sense unless I specifically say that I am not.

It is worth noting that although a Marshall
improvement is usually not a Pareto improvement, the adoption of a
general policy of "Wherever possible, make Marshall improvements" may
come very close to being a Pareto improvement. In one case, the
Marshall improvement benefits me by $3 and hurts you by $2; in
another it helps you by $6 and hurts me by $4; in another . . . Add
up all the effects and, unless one individual or group is
consistently on the losing side, everyone, or almost everyone, is
likely to benefit. That is one of the arguments for such a policy and
one of the reasons to believe that economic arrangements that are
Marshall efficient are desirable.

EFFICIENCY AND
THEBUREAUCRAT-GOD

In describing some economic arrangement as
efficient or inefficient, we are comparing it to possible
alternatives. This raises a difficult question: What does "possible"
mean? One could argue that only that which exists is possible. In
order to get anything else, some part of reality must be different
from what it is.

But one purpose of the concept of efficiency is to
help us decide how to act--how to change reality to something
different than it now is. So any practical application of the idea of
efficiency must focus on some particular sorts of changes. What sorts
of changes are and should be implicit in the way we use the
term?

One could argue that however well organized the
economy may be, it is still inefficient. A change such as the
invention of cheap thermonuclear power or a medical treatment to
prevent aging would be an unambiguous improvement--and surely some
such change is possible. That might be a relevant observation--if
this were a book on medicine or nuclear physics. Since it is a book
on economics, the sorts of changes we are concerned with involve
using the present state of knowledge (embodied for our purposes in
production functions, ways of converting inputs to outputs) but
changing what is produced and consumed by whom.

One way of putting this that I have found useful
is in terms of a bureaucrat-god. A bureaucrat-god has all of
the knowledge and power that anyone in the society has. He knows
everyone's preferences and production functions and has unlimited
power to tell people what to do. He does not have the power to make
gold out of lead or produce new inventions. He is benevolent; his
sole aim is to maximize welfare in Marshall's sense.

An economic arrangement is efficient if it cannot
be improved by a bureaucrat-god. The reason we care whether an
arrangement is efficient is that if it is, there is no point in
trying to improve it. If it is not efficient, there still may be no
practical way of improving it--since we do not actually have any
bureaucrat-gods available--but it is at least worth
looking.

At this point, it may occur to you that while
efficiency as I have defined it is an upper bound on how well an
economy can be organized, it is not a very useful benchmark for
evaluating real societies. Real societies are run not by omniscient
and benevolent gods but by humans; however rational they may be, both
their knowledge and their objectives are mostly limited to things and
people that directly concern them. How can we hope, out of such
components, to assemble a system that works as well as it would if it
were run by a bureaucrat-god? Is it not as inappropriate to use
"efficiency" in judging the performance of human institutions as it
would be to judge the performance of race cars by comparing their
speed to its theoretical upper bound--the speed of light?

The surprising answer is no. As we will see in
Chapter 16, it is possible for institutions that we have already
described, institutions not too different from those around us in the
real world, to produce an efficient outcome. That is one of the most
surprising--and useful--implications of economic theory.

WARNING

While the way in which this textbook teaches
economics is somewhat unconventional, the contents--what is
taught--are not very different from what many other economists
believe and teach. This chapter is the major exception. While Alfred
Marshall was, in other respects, a much more important figure in the
history of economics than Vilfredo Pareto, Marshall's solution to the
problem of deciding what is or is not an improvement has largely
disappeared from modern economics; virtually all elementary texts
teach the Paretian approach. Both the Marshallian approach and the
Paretian, as it is commonly applied, have, under most circumstances,
the same implications for what is or is not efficient. What differs
is the justification given for the conclusions that both
imply.

I am by no means the only contemporary economist
who feels uncomfortable with the Paretian approach, but I may be the
first to put that discomfort, and the Marshallian solution, into a
textbook. In that respect, this chapter is either "on the frontier"
or "out of the mainstream," according to whether one does or does not
agree with it.

OPTIONAL SECTION

SOCIAL WELFARE AND
THE

ARROW IMPOSSIBILITY
THEOREM

Earlier in this chapter, I mentioned that one
"solution" to the problem of evaluating outcomes that affect
different people is to assume that there exists a social welfare
function--a procedure for ranking such outcomes--without actually
specifying what it is. This is somewhat like the way we handle
individual preferences; we assume a utility function that allows the
individual to rank alternatives that affect him, although we have no
way of knowing exactly what that function is.

But in the case of the utility function, although
we cannot predict it, we can observe it by observing what choices the
individual actually makes. There seems to be no equivalent way to
observe the social welfare function, since there is no obvious sense
in which societies make choices. We could try to describe a
particular set of political institutions in this way, substituting
"the outcome of the political process" for "what the individual
chooses." But while this might be a useful way of analyzing what
those institutions will do, it tells us nothing about what
they should do--unless we are willing to assume that the two
are identical. This leaves the social welfare function as an abstract
way of thinking about the question, with no way of either deducing
what it should be or observing what it is.

Even as an abstract way of thinking about the
problem, the social welfare function has problems; not only is it an
unobservable abstraction, it may well be a logically inconsistent
one. To explain what I mean by that, I will start by showing how we
can eliminate a particular candidate for a social welfare
function--majority rule. I shall then tell you about a similar and
much stronger result that eliminates a broad range of possible social
welfare functions.

A social welfare function is supposed to be a way
of ranking outcomes that affect more than one person; it is intended
to be the equivalent, for a group, of an individual's utility
function. There are two different ways in which one could imagine
constructing a social welfare function. One is to base social
preferences on individual preferences, so that what the society
prefers depends, perhaps in some complicated way, on what all of the
individuals prefer. The other is to have some external standard: what
is good according to correct philosophy, in the mind of God, or the
like. Economists, knowing very little about either the mind of God or
correct philosophy, are reluctant to try the second alternative, so
they have usually assumed that social preferences are built on
individual preferences.

One advantage to defining social preferences in
terms of individual preferences is that individual preferences
express themselves in individual actions. Perhaps if we could set up
the right set of social institutions, the choices made by all the
individual members of society would somehow combine to produce the
"socially preferred" outcome for the society. That, in a way, is the
idea of democracy: Let each individual vote for what he prefers and
hope that the outcome will be good for the society. Seen in this way,
majority rule is a possible social welfare function. For each pair of
alternatives, find out which one more people like and label that the
socially preferred choice.

One problem with this was pointed out several
centuries ago by Condorcet, a French mathematician. Majority vote
does not produce a consistent set of preferences. Consider Table
15-1, which shows the preferences of three individuals among three
outcomes. Individual 1 prefers outcome A to outcome B and outcome B
to outcome C; Individual 2 prefers B to C and C to A; Individual 3
prefers C to A and A to B. Suppose we consider a society made up of
only these three people and try to decide which outcome is preferred
under majority rule. In a vote between A and B, A wins two to one,
since Individuals 1 and 3 prefer it. In a vote between B and C, B
wins two to one, since 1 and 2 prefer it. It appears that we have a
social ranking; A is preferred to B and B to C.

Individual

Ranking

1

2

3

First

A

B

C

Second

B

C

A

Third

C

A

B

Table 15-1

If A is preferred to B and B to C, then A must
also be preferred to C. But it is not. If we take a vote between A
and C, Individual 1 votes for A but both 2 and 3 vote for C--so C
wins. We have a system of social preferences in which A is preferred
to B, B to C, and C to A! This is what mathematicians call an
intransitive ordering; obviously it does not produce a
consistent definition of what is socially preferred.

This Condorcet Voting Paradox eliminates
majority rule as a possible definition of social welfare. A similar
and much more general result proved by Kenneth Arrow, called the
Arrow Impossibility Theorem, eliminates practically everything
else. Arrow made a few plausible assumptions about what a social
welfare function must be like and then proved that no possible
procedure for going from individual preferences to social preferences
could satisfy all of them.

What are the assumptions? One is nondictatorship;
the social welfare function cannot simply consist of picking one
individual and saying that whatever he prefers is socially preferred.
Another has the long name independence of irrelevant
alternatives. It says that if the social welfare function,
applied to individuals with a particular set of individual
preferences, leads to the conclusion that alternative A is preferred
to alternative B, then a change in preferences that does not affect
anyone's preferences between A and B cannot change the social
preference between A and B. Another assumption is that social
preferences are positively related to individual preferences; if some
set of individual preferences lead A to be preferred to B, a change
in the preference of one of the individuals from preferring B to
preferring A cannot make the social preference change in the other
direction. The society cannot switch to preferring B as the result of
an individual switching to preferring A. Finally the social welfare
function must lead to a consistent set of preferences; if A is
preferred to B and B to C, then A must be preferred to C.

What Arrow proved was that no rule for going from
individual preferences to group preferences could be consistent with
all of those assumptions.

Economics Joke #2: A physicist, a
chemist, and an economist were shipwrecked on a desert island.
After a while, a case of canned beans drifted to shore; the three
began discussing how to open the cans. The chemist (a physical
chemist) suggested that if they started a fire and put a can of
beans on it, he could calculate at what point the resulting
pressure would burst the can. The physicist said that he could
then calculate the trajectory the beans would take as they spouted
out of the burst can and put a clean palm leaf down for them to
land on. "That's too much trouble," the economist said. "Assume we
have a can opener." (This is a joke about the social welfare
function.)

The Arrow Impossibility Theorem does not quite
prove that a social welfare function is logically impossible. For one
thing, the theorem only applies to social preferences based on
individual preferences; a social welfare function that says,
"Socially preferred means what God wants" or "Socially preferred
means what a philosopher can prove that we all ought to want," is not
eliminated by the theorem. Furthermore it applies to social welfare
functions based on preferences but not to those based on utility
functions. The only form in which utility functions are observable is
as preferences; we can observe that you prefer a cookie to a Diet
Coke (because given the choice, you take the cookie), but we cannot
observe by how much you prefer it. Even the Von Neumann version of
utility discussed in the optional section of Chapter 13, while
allowing quantitative statements about my preferences, does not allow
quantitative comparisons between my preferences and yours.

If, in deciding what was socially preferred, we
could use not only the fact that I preferred A to B but also that I
preferred A to B by seven utiles and B to C by two, while you
preferred B to A by one utile and C to B by three, the Impossibility
Theorem would no longer hold. In this case, the obvious social
welfare function would be total utility: Add up everyone's utility
for each outcome and use the sum as your social welfare function.
This rule for defining what is desirable, called utilitarianism by
philosophers, played an important role in the development of
economics (and philosophy). Alfred Marshall, for instance, was a
utilitarian who proposed what I have called Marshall efficiency as an
approximate rule for maximizing the (unobservable) total
utility.

AMBIGUITIES IN THE CONCEPT OF
IMPROVEMENT

For most purposes, improvement in Marshall's sense
provides an adequate working rule for applying our rather vague ideas
of what is or is not a net improvement, but there are situations in
which it can lead to apparently inconsistent results. Imagine a
society of two people, you and me. There is one good in this society
that is immensely valuable: a life-extension pill that doubles the
life expectancy of whichever one of us takes it. There are also other
goods. Suppose we want to use Marshall's approach to decide which of
us should have the pill.

If I have the pill, there is no sum you could
offer me that would make me willing to give it up; the pill plus the
goods I already have are worth more to me than all of the other goods
(mine plus yours) without the pill. The maximum you would be willing
to offer me for the pill is less than all of your goods, since there
is no advantage to you in taking the pill and then starving to death.
So the dollar value of the pill to me (the amount I would have to be
paid to give it up) is greater than its dollar value to you (the
amount you would pay to get it). Leaving me with the pill is then, by
Marshall's criterion, the preferred outcome; more precisely, taking
the pill away from me is not an improvement.

But suppose we start with you having the pill.
Following exactly the same argument, we find that leaving you with
the pill is the preferred outcome! The problem is that since the pill
is immensely valuable to both of us, whoever has it is, in effect,
much wealthier than if he did not. He is wealthier not because he has
more money but because he already has the most important thing that
he would want money to buy. Since he is wealthier, the utility of
money to him is less. So the money value of anything to him--what he
would be willing to pay to get other goods or what he would have to
be paid to give up the pill--is higher than it would be if he did not
start out owning the pill. Since we are measuring utility by how much
money (or goods) someone is willing to give to get something or
willing to accept in exchange for giving something up, we get
different results according to who we assume starts off with the
pill.

Most applications of Marshall's definition of
improvement do not involve this problem. If, for example, we consider
the desirability of tariffs, it probably does not matter whether we
start by assuming that tariffs exist and ask how people would be
affected by abolishing them (measuring the amount of gains and
injuries by their dollar equivalents) or start by assuming they do
not exist and ask how people would be affected by imposing them. One
reason it would not matter is that most of the gains and losses are
themselves monetary; the dollar value to you of a $1 increase in your
income is the same however rich you are. Another reason is that even
if some of the gains and losses were nonmonetary, the abolition (or
institution) of tariffs would have a relatively small effect on most
people's income, hence a small effect on the monetary equivalent to
them of some nonmonetary value.

This sort of problem is not limited to the
Marshallian approach. Under the strict Pareto definition (an
improvement means a Pareto improvement: someone is benefited and no
one is hurt), most alternatives are incomparable; not only is there
no way of deciding who should get the life-extension pill, there is
no way of deciding whether tariffs should be abolished. As long as
the abolition makes one person worse off, it is not a Pareto
improvement. Under the "potential Pareto" criterion (a change is an
improvement if there is some set of transfers from gainers to losers
that, combined with the change, results in a Pareto improvement), one
gets exactly the same problems as with Marshall's
criterion.

PROBLEMS

1. In Figure 15-3a, the production possibility set
for a worker working eight hours per day is shown as the shaded area.
Which labeled points are output efficient? Which labeled points are
output superior to point A?

Opportunity sets for Problems
1-3.

2. In Figure 15-3b, the shaded area shows possible
outcomes in terms of the resulting divisions of income between two
people, John and Lisa; nobody else exists. Which labeled points are
Pareto efficient? Which are Marshall efficient? Which are Pareto
superior to point A? Which are Marshall superior to point A? Which
are "potentially Pareto superior" to point A?

3. Figure 15-3c is similar to Figure 15-3b. What
do you think is the significance of the difference between the shapes
of the shaded areas in Figures 15-3b and 15-3c? (Warning: This
question requires original thought.)

4. The shaded area on Figure 15-4a is the
possibility set for a worker working eight hours a day cutting down
trees and making sawdust. Which labeled points are output efficient?
Which are output superior to A? to B? to D? Which labeled points is A
superior to? What about D?

Figure 15-4a Figure 15-4b

Figures for problems
4-6.

5. The shaded area on Figure 15-4b shows possible
outcomes in terms of their effect on the incomes of two people, Ann
and Bill; nobody else exists. Which labeled points are Pareto
efficient? Which are Marshall efficient? Which are Pareto superior to
point A? Which are Marshall superior to point A? Which are
potentially Pareto superior to point A?

6. Draw the Pareto-efficient part of Figure
15-4b.

7. In this chapter, I gave one example of a
Marshall improvement that many people would consider undesirable: a
change that benefited a rich man by $10 and injured a poor man by $9.
Give at least two other examples of Marshall improvements that many
people (including well-informed people not themselves affected) would
consider undesirable, where the reason for the conflict between the
Marshall criterion and desirability does not depend on differences in
income or wealth among the people affected.

8. One obvious objection to Marshall's definition
of improvement is that we should take into account distributional
effects: if a policy is a slight Marshall worsening but helps the
poor it might still be desirable from a utilitarian standpoint. In
order to take account of such effects, we must know what they are;
this is not always easy. For each of the following policies, first
describe what you think its distributional effect is (makes incomes
more equal or makes incomes less equal) then give at least one reason
why it might have the opposite effect.

a. Agricultural price supports.

b. Minimum wage laws.

c. Tax-supported state universities.

9. The government imposes a tax of $0.10/pound on
artichokes; the money is used to give everyone $5 for Christmas.
Assume that people are not all identical. Is the law a Pareto
improvement? A Marshall improvement? Would its abolition be a Pareto
improvement? A Marshall improvement? Explain.

10. Do Problem 9 on the assumption that people are
all identical.

11. The government imposes a $0.10/pound tax on
artichokes; the supply and demand curves are shown in Figure 15-5.
The money is used to finance research on thermonuclear power. Each
dollar spent on such research produces two dollars worth of benefits.
Answer as in Problem 9.

Supply and demand for artichokes-Problem
11.

12. The situation is as in Problem 11, except that
you can vary the level of tax. How would you find the (Marshall)
efficient level? Approximately what is it? (Warning: This is a hard
problem. A verbal explanation requires original thought. A numerical
answer may require either more mathematics than some of you have or a
good deal of trial and error.)

FOR FURTHER READING

The ideas I have described as "Marshall
improvement" and "Marshall efficiency" are more commonly derived from
the idea of a potential Pareto improvement and referred to as the
Hicks/Kaldor criterion. For the original, interesting, and
readable discussion of those ideas, you may want to look at Alfred
Marshall, Principles of Economics, (8th. ed.; London:
Macmillan, 1920), Chapter VI.

Some other important papers on the Hicks/Kaldor
criterion include: Nicholas Kaldor, "A Note on Tariffs and the Terms
of Trade," Economica (November, 1940); John R. Hicks, "The
Foundations of Welfare Economics," Economic Journal (December,
1939); and Tibor Scitovsky, "A Note on Welfare Propositions in
Economics," Review of Economic Studies (November,
1941).

The Arrow Impossibility Theorem is proved in
Kenneth Arrow, Social Choice and Individual Values, (2nd ed.;
New Haven, CT: Yale University Press, 1970).

At several points in this chapter, I have asserted
that the Marshallian and potential Paretian (Kaldor/Hicks)
definitions of efficiency lead to the same conclusion; any situation
that is efficient by one definition is efficient by the other. That
is not quite true, as I discovered after the first edition of this
book was published. For a description of circumstances under which an
outcome can be Kaldor efficient but not Marshall efficient, see:
David Friedman, "Does Altruism Produce Efficient Outcomes? Marshall
vs Kaldor," Journal of Legal Studies Vol. XVII, (January
1988).